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A002200
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Primes of the form 2^q*3^r*5^s + 1.
(Formerly M0654 N0242)
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5
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2, 3, 5, 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 101, 109, 151, 163, 181, 193, 241, 251, 257, 271, 401, 433, 487, 541, 577, 601, 641, 751, 769, 811, 1153, 1201, 1297, 1459, 1601, 1621, 1801, 2161, 2251, 2593, 2917, 3001, 3457, 3889, 4001, 4051, 4801, 4861
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OFFSET
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1,1
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REFERENCES
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M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 53.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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up=10^6; a=1; Sort[Reap[While[ a<up, b=a; While[ b<up, c=b; While[ c<up, If[ PrimeQ[ c+1], Sow[ c+1]]; c *= 5]; b *= 3]; a *= 2]][[2, 1]]] (* Giovanni Resta, Jul 18 2017 *)
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PROG
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(PARI) { default(primelimit, 16600000); n=0; forprime (p=2, 16600000, m=p-1; p2=p3=p5=0; s=m; r=0; while(r==0, q=s\2; r=s-2*q; s=q; if(r==0, p2++)); s=m; r=0; while(r==0, q=s\3; r=s-3*q; s=q; if(r==0, p3++)); s=m; r=0; while(r==0, q=s\5; r=s-5*q; s=q; if(r==0, p5++)); if (m == 2^p2*3^p3*5^p5, n++; write("b002200.txt", n, " ", p)); if (n >= 200, break); ); } \\ Harry J. Smith, May 25 2009
(PARI) { n=5000; cache=10^5; v=vector(cache); x2=2; x3=3; x5=5; i=j=k=1; v[1]=1; for(m=2, cache, v[m]=t=min(x2, min(x3, x5)); if(x2==t, x2=2*v[i++]); if(x3==t, x3=3*v[j++]); if(x5==t, x5=5*v[k++]); ); i=0; c=0; while(c<n, i++; if(isprime(v[i]+1), c++; print(c" "v[i]+1))); } \\ Jean-Marie Madiot, Jul 17 2017
(Magma) [p: p in PrimesUpTo(5000) | forall{d: d in PrimeDivisors(p-1) | d le 5}]; // Bruno Berselli, Sep 24 2012
(GAP)
K:=10^7;; # to get all terms <= K.
A:=Filtered([1..K], IsPrime);;
B:=List(A, i->Factors(i-1));;
C:=[];; for i in B do if Elements(i)=[2] or Elements(i)=[2, 3] or Elements(i)=[2, 5] or Elements(i)=[2, 3, 5] then Add(C, Position(B, i)); fi; od;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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